Eight teams compete in a tournament. Each pair of teams plays exactly one game against each other. There are no ties. If the two possible outcomes of each game are equally likely, what is the probability that every team loses at least one game and wins at least one game?
I found this question on 2017 Fermat Competition of Waterloo University. The original solution seems a bit wordy and redundant. I wonder if there is a way to solve the probability in more simplified approaches? Original Solution (Page 8)